Cremona's table of elliptic curves

690 = 2 · 3 · 5 · 23

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 23+	Signs for the Atkin-Lehner involutions
Class	690g	Isogeny class
Conductor	690	Conductor
∏ cp	28	Product of Tamagawa factors cp
Δ	49503729150000000 = 27 · 316 · 58 · 23	Discriminant
Eigenvalues	2- 3+ 5+  0  0  6  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-101131,-6258247]	[a1,a2,a3,a4,a6]
j	114387056741228939569/49503729150000000	j-invariant
L	1.9492533689955	L(r)(E,1)/r!
Ω	0.27846476699936	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5520ba3 22080bi3 2070i3 3450j4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 690g4

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	+	+	0	0	6	2	0	+	6	8	10	-6	-8	8	-6	-4	-6	8	-8	10	-8	-8	-6	18

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Quadratic twists for elliptic curve 690g4

-4	8	-3	5	-7	-11	13	-23
5520ba3	22080bi3	2070i3	3450j4	33810de3	83490d3	116610i3	15870z3

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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